Answer :
To determine which set of side lengths could represent congruent triangles, we need to understand what congruent triangles are. Congruent triangles have the same shape and size, which means that their corresponding sides and angles are equal. For side lengths, this implies that we are looking for sets where some or all of the sides are the same length.
Now, let's analyze each set of side lengths:
1. Set 1: [tex]$10 m, 10 m, 14 m$[/tex]
- In this set, there are two sides that are equal in length: 10 m and 10 m. This set can represent a congruent triangle because having two sides of the same length is a characteristic of an isosceles triangle, which can be congruent to another isosceles triangle with the same side lengths.
2. Set 2: [tex]$10 m, 14 m, 14 m$[/tex]
- Here, two sides are equal to 14 m. Like the first set, this can also form a congruent triangle. This is an isosceles triangle, and having two identical side lengths is sufficient for congruency with a similar triangle.
3. Set 3: [tex]$42 m, 42 m, 69 m$[/tex]
- This set also has two sides that are equal in length, which are 42 m and 42 m. These two identical sides suggest that the set can describe a congruent triangle.
4. Set 4: [tex]$42 m, 69 m, 69 m$[/tex]
- Similarly, this set has two sides that are equal, which are 69 m and 69 m. Thus, it can also form a congruent triangle since it maintains the isosceles property.
In summary, all sets given could possibly come from congruent triangles because they all have at least two sides that are equal in length. This characteristic allows them to be congruent with another triangle having the same set of side lengths.
Now, let's analyze each set of side lengths:
1. Set 1: [tex]$10 m, 10 m, 14 m$[/tex]
- In this set, there are two sides that are equal in length: 10 m and 10 m. This set can represent a congruent triangle because having two sides of the same length is a characteristic of an isosceles triangle, which can be congruent to another isosceles triangle with the same side lengths.
2. Set 2: [tex]$10 m, 14 m, 14 m$[/tex]
- Here, two sides are equal to 14 m. Like the first set, this can also form a congruent triangle. This is an isosceles triangle, and having two identical side lengths is sufficient for congruency with a similar triangle.
3. Set 3: [tex]$42 m, 42 m, 69 m$[/tex]
- This set also has two sides that are equal in length, which are 42 m and 42 m. These two identical sides suggest that the set can describe a congruent triangle.
4. Set 4: [tex]$42 m, 69 m, 69 m$[/tex]
- Similarly, this set has two sides that are equal, which are 69 m and 69 m. Thus, it can also form a congruent triangle since it maintains the isosceles property.
In summary, all sets given could possibly come from congruent triangles because they all have at least two sides that are equal in length. This characteristic allows them to be congruent with another triangle having the same set of side lengths.
